The triangle formed by the points (2, 7), (4, -1) and (-2, 6) will be -

Explanation

The three points of the triangle respectively. A = (2, 7), B = (4, –1), C = (–2, 6) Length of first side, AB $$= \sqrt{(4-2)^2 - (-1-7)^2}$$ $$= \sqrt{2^2 + (-8)^2} = \sqrt{68}$$ Length of second side, BC $$= \sqrt{(-2-4)^2 + (+6+1)^2}$$ $$= \sqrt{(-6)^2 + 7^2} = \sqrt{85}$$ Length of the third side, CA $$= \sqrt{(-2-2)^2 + (6-7)^2}$$ $$= \sqrt{(-4)^2 + (-1)^2} = \sqrt{17}$$ According to Pythagoras theorem- BC² = AB² + CA² $(\sqrt{85})^2 = (\sqrt{68})^2 + (\sqrt{17})^2$ $85 = 85$ i.e. $\Delta$ABC is a right angled triangle.